Loops in AdS: From the Spectral Representation to Position Space II

Abstract

We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-$N$ conformal Gross Neveu model on $Ad{S}_3$. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].

arXiv commentminor corrections, 36 pages, 11 figures

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• An Elliptic One-Loop Amplitude in Anti-de-Sitter Space
• 1d Conformal Field Theory and Dispersion Relations
• Information Geometry and Holographic Correlators
• Constructing CFTs from AdS flows
• Partition functions for $U(1)$ vectors and phases of scalar QED in AdS